Dr Bevan's ultimate Tuba Bible** deals with this profile question of course (pp189 et al) And, just for this topic, see the Moritz 1838 Basstuba with its longer mouthpipe on p 205 and the facing profile drawings.
I remember meeting an American in the Bayreuth staff restaurant in the early Jurrasic era [1972/3??] who worked for Hirschbrunner. He was just back from torturing a new CC tuba by stringing out straight the entire poor instrument inside an aircraft hangar in Switzerland!! I asked him how they could reach the valves. He did not laugh but explained very patiently about profile and silhouettes and taper and tuning slides before and after the valve block. I could see the point, but it was definitely not science but rather an empirical experiment.
**Every serious tuba player must, of course, learn this off by heart, the ultimate book on the tuba. Everyone must buy and read it at least 100 times: It should be required reading for all students. If you have not read it you simply do not know where you are coming from or going to. Dr Clifford Bevan's 'The Tuba Family', http://http://www.piccolopress.info/tuba_family.htm" target="_blank" target="_blank" £35 - $45 .
[Again, never ever buy this from the

